Finding the best individual online math tutor for students can be a challenge, but that’s nothing compared to some of the challenges that these young learners face as they successfully battle their way through middle school and high school math classes. By the time students have reached grade 7, they will become familiar with using numbers, solving equations, and recognizing, measuring, and drawing conclusions from shapes.
Although it may sound childish, studying shapes is vitally important to a child’s ability to develop a mathematical brain capable of thriving in math class, all the way to the Math SAT and beyond. One shape that comes up more than most – and that teaches us as much if not more than any other – is the triangle.
We all know triangles have 3 sides and 3 corners, but what else do we know? Can the shapes be different lengths? Do they have to be the same length? How many angles are there and how do we measure them?
One of these questions that we do know the answer to is how many total degrees the angles on a triangle sum to. Proving this fact is a hurdle that grade 7 students must do, so let’s take a look at this problem, what it means, and how we solve it.
What is The Angle Sum Property
Sometimes known as the sum of the angle measures in a triangle, the angle sum property tells us that, in a triangle, the three interior angles always add up to 180°. This basically means that no matter what difference there is in the size of the angles, regardless of the lengths of the sides, the three interior angles of a triangle will always be 180°.
To show you this is always true, take a look at this page with an interactive triangle that you can pull and change to alter the angles, and you will see they will still add up to 180°. You should try this several times, to truly see that triangles and their side lengths can be wildly different from each other, but their interior angles will always sum to 180°.
Doing this – methodically proving that something is true – is a fantastic analytical skill that kids can learn when they are still young, and can be applied to virtually any school subject to further their knowledge and understanding. Now that we know what this necessary proof means, how do we go about proving it?
Proving The Angle Sum Property
Proving the angle sum theory is not as difficult or as complicated as you may think. To prove the angle sum theory, we rely on some previous lessons on angles and triangles, as well as some of the knowledge that we gained when studying parallel lines.
To solve the angle sum property: consider the following image:
With this image to help us, things become a lot less complicated. We can see that we have a triangle with angles A, B, and C, and we have a broken straight line touching the triangle only at one corner.
The broken straight line that touches the triangle is running parallel to the base of the triangle.
We can see that:
- angles A are the same as each other
- angles B are the same as each other
We can also see that A + C + B makes a full 180° rotation from one side of the straight line to the other – this tells us that A + B + C = 180°.
Now that you know what the angle sum property is, and how to prove it, you can begin to use the knowledge you’ve gained to solve other problems that you may face regarding angles and triangles. For example, you could use this proof to solve for one missing angle in a triangle, when you have the value of the other two angles.
OMC Grade 7 Math Courses
At OMC, we pride ourselves on the results we deliver. Our students get the best, personalized, one-to-one math tutoring available anywhere in the world. Our qualified teachers bring a wealth of knowledge and experience, offering comprehensive courses for all grades from fifth onwards and right through to our intensive Math SAT preparation courses. No matter your child’s needs, age, or mathematical ability, OMC is the right place to help them reach their potential and hit their goals in math class.